standard deviation or the square root of the variance is a measure applied to the annual rate of return of an investment to measure the investment volatility. every time you buy a stock or a mutual fund, you're weighing its expected return against its inherent risk. the past gains or losses of an investment are fairly easy to look up but gauging risk is a little trickier. applying the standard deviation formula will show how much an investment's price has gone up or down in the past and therefore helps evaluating future outcomes. take, for example, a security where we analyze five periods of the following stock returns. 2% in january, 7.5% in february, 1% in the next month, 6% and 1.5% finally in may. to find the standard deviation for a security, find the average historical return, which is 3.6%, and subtract the returns from each month, square them and find the sum. next, we divide that sum by the number of observations minus one. in this case, it will be four. leaving us with the result of 8.675. taking the square root of that number, we are left with a standard deviation of 2.9. the calculation can be particularly helpful when looking at similar investments in the same asset class. if one investment has a higher standard deviation than the other, that investment is more volatile. note that past volatility or lack thereof doesn't perfectly predict future returns. a stock that has been consistent for months or even years may suddenly experience sharp fluctuations.